How to solve for quadratic equations with inequalities?

Final answer:

To convert 6 7/9% to a decimal, we change the mixed number to an improper fraction, divide by 100 and round to the nearest thousandth, resulting in approximately 0.068.

Explanation:

To find the decimal equivalent of 6 7/9%, we must first convert the mixed number to an improper fraction and then to a decimal. To convert 6 7/9% to an improper fraction, we multiply the whole number 6 by the denominator 9 and add the numerator 7 to get 7 + (6 × 9) = 7 + 54 = 61. Then we place 61 over the original denominator to obtain 61/9. The percentage sign indicates that we are dealing with a part out of 100, so we must divide 61/9 by 100 or, equivalently, multiply by 1/100.

Therefore, the calculation to convert the percentage to a decimal is: (61/9) × (1/100) = 61/900. Using a calculator, or performing the division manually, gives us approximately 0.0677777....

Finally, to round this to the nearest thousandth, we would look at the fourth decimal place (which is 7 in this case). Since 7 is greater than 5, we round up the third decimal place, resulting in 0.068.

This is irrelevant, but was THAT many exclamation points necessary?

Anyway, these aren't that hard, you gotta just use your brain a bit. These problems use a bit of simple common sense if you put 2-and-2 together and look into it. Look for signs and just use your head, it's hard to explain but just try. ^^

The standard form of the equation  is:

                  [tex]x=8y^2-16y-7[/tex]

We know that the standard form of a quadratic equation is given by the expression:

[tex]x=ay^2+by+c[/tex]

where a,b and c are real numbers.

and a≠0

Here we are given the  vertex form of the equation of a parabola by:

[tex]x=8(y-1)^2-15[/tex]

Now, on expanding the parentheses term by using the formula:

[tex](a-b)^2=a^2+b^2-2ab[/tex]

Here a=y and b= 1

Hence, we have:

[tex]x=8(y^2+1-2y)-15\\\\i.e.\\\\x=8\times y^2+8\times 1-2y\times 8-15\\\\i.e.\\\\x=8y^2+8-16y-15\\\\i.e.\\\\x=8y^2-16y+8-15[/tex]

( Since, in the last step we combined the constant term i.e. 8 and -15 )

Hence, we get the standard form of the equation as:

[tex]x=8y^2-16y-7[/tex]

8.2% = 0.082

50 * 0.082 = 4.1

the answer is 4.1

The acceptable circumferences for a woman's basketball range from 28.5 inches to 29 inches.

To find the acceptable circumferences for a woman's basketball, we need to consider the ideal circumference and the allowable variation. The ideal circumference is 28.75 inches and the actual circumference can vary by at most 0.25 inches. So, the acceptable circumferences can be found by adding and subtracting the maximum allowable variation from the ideal circumference:

Acceptable circumference = 28.75 ± 0.25 inches

This means the acceptable circumferences for a woman's basketball range from 28.5 inches to 29 inches.

Answer:

the answer is B

Step-by-step explanation:

Answer:

The correct answer is C.

Step-by-step explanation:

This can be done using complex numbers and its relations with plane geometry. The endpoints of the segment are X(-6,2) and Y(-1,-3). These points can be seen as complex numbers, just recall the geometric interpretation of complex numbers.

So, the complex counterpart of [tex]X(-6,2) is x=-6+2i[/tex], and the complex counterpart of [tex]Y(-1,-3) = -1-3i[/tex]. Moreover, a rotation about the origin has an interpretation as multiplication by a complex number of modulus 1. In this particular case, a rotation of 90 degrees is equivalent to multiply by the complex unit: [tex]i=\sqrt{-1}[/tex].

Then,

[tex] x' = (-6+2i)\times i = -2-6i[/tex] which gives the point [tex]X'(-2,-6)[/tex]

[tex] x' = (-1-3i)\times i = 3-1i[/tex] which gives the point [tex]Y'(2,-1)[/tex].

The other option is to use a software to make geometrical constructions as Geogebra. Bellow there is an image attached made with Geogebra with the solution of the exercise.

The required values are x = 60 and y = 30 for the given parallelogram.

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal. A parallelogram is a square and a rhombus is a square.

The parallelogram is represented in the given figure

A parallelogram has two pairs of adjacent sides that are congruent.

As per the given figure, we have

x + 5x - 180 = 180

6x = 360

x = 360/6

Apply the division operation, and we get

x = 60

2y + 4y = 180

Apply the addition operation, and we get

6y = 180

y = 180/6

y = 30

Thus, the required values are x = 60 and y = 30

Learn more about parallelograms here:

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When calculating the change in internal energy (δe) using the First Law of Thermodynamics, first convert all units to the same kind, then apply the formula δe = q + w. In this case, the answer is -0.07 kJ or -70 J.

This is a Chemistry question involving the calculation of change in internal energy (δe) using the First Law of Thermodynamics, which states that the change in internal energy is equal to heat (q) added to the system plus the work (w) done on the system. Specifically, the formula is: δe = q + w.

        -830 J * (1 kJ / 1000 J) = -0.83 kJ.

Therefore, using two significant figures, the answer is -0.07 kJ or -70 J.

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The change in internal energy (ΔE) is -0.07 kJ. Since ΔE is negative, this indicates that the system has lost internal energy.

Given:

q = 0.764 kJ

w = -830 J

We can calculate the change in internal energy (ΔE) using the following equation:

ΔE = q + w

where:

ΔE is the change in internal energy (kJ)

q is the heat absorbed by the system (kJ)

w is the work done by the system (kJ)

First, convert the work from joules to kilojoules:

w = -830 J * (1 kJ/1000 J) = -0.830 kJ

Now, plug in the values for q and w to calculate ΔE:

ΔE = 0.764 kJ + (-0.830 kJ) = -0.066 kJ

Round the answer to two significant figures:

ΔE ≈ -0.07 kJ

Therefore, the change in internal energy (ΔE) is -0.07 kJ. Since ΔE is negative, this indicates that the system has lost internal energy.

Final answer:

There were 113 people who bought a ticket but did not show up to the concert, calculated by subtracting the number of attendees (587) from the total tickets sold (700).

Explanation:

To determine how many people bought a ticket but did not attend the concert, you would subtract the number of people who attended from the total number of tickets sold. In this case, 700 tickets were sold and only 587 people attended. So, the calculation would be:

700 tickets sold - 587 attendees = 113 people who did not attend

Thus, 113 people bought a ticket but did not show up to the concert.

Answer:

[tex]x1=\frac{-2(+)2i\sqrt{2}} {3}[/tex]

[tex]x2=\frac{-2(-)2i\sqrt{2}} {3}[/tex]

Step-by-step explanation:

we have

[tex]-3x^{2} -4x-4=0[/tex]

Rewrite (Multiply by [tex]-1[/tex] both sides)

[tex]3x^{2}+4x+4=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]3x^{2}+4x+4=0[/tex]

so

[tex]a=3\\b=4\\c=4[/tex]

substitute

[tex]x=\frac{-4(+/-)\sqrt{4^{2}-4(3)(4)}} {2(3)}[/tex]

[tex]x=\frac{-4(+/-)\sqrt{-32}} {6}[/tex]

remember that

[tex]i=\sqrt{-1}[/tex]

[tex]x=\frac{-4(+/-)4i\sqrt{2}} {6}[/tex]

Simplify

[tex]x=\frac{-2(+/-)2i\sqrt{2}} {3}[/tex]

[tex]x1=\frac{-2(+)2i\sqrt{2}} {3}[/tex]

[tex]x2=\frac{-2(-)2i\sqrt{2}} {3}[/tex]

Answer:

C.Less than $712.50

Step-by-step explanation:

Given details are :

Loan amount = $190,000

Rate = 4.5% or 0.045 compounded monthly.

Time = [tex]30\times12=360[/tex] months

Monthly payments are = $962.70

First month interest = $712.50

I have calculated this using excel sheet and the answer is - C.Less than $712.50 .

Please find attached the excel sheet to see the working. You can see the highlighted interest that is less than first month interest.

Answer:Less than $712.50

Step-by-step explanation:

The two numbers are 31 and 19, where 31 is the larger number and 19 is the smaller number which is 12 less than the larger number.

The sum of two numbers is given to be 50, and the question states that the smaller number is 12 less than the larger number. To find these numbers, let's denote the larger number as x and the smaller number as x - 12. According to the problem, the sum of these two numbers is 50, so we can write the equation:

x + (x - 12) = 50

Simplifying the equation gives us:

2x - 12 = 50

Adding 12 to both sides gives us:

2x = 62

Dividing both sides by 2 gives us:

x = 31

Now that we know the larger number is 31, we can find the smaller number by subtracting 12:

x - 12 = 31 - 12

x - 12 = 19

Therefore, the two numbers are 31 and 19.

Final answer:

The standard form of the equation y = (3/8)x - 4 is 8y - 3x = -32.

Explanation:

The standard form of the equation y = (3/8)x - 4 is written as 8y - 3x = -32.

To convert a linear equation from slope-intercept form (y = mx + b) to standard form (Ax + By = C), you need to multiply the entire equation by the common denominator of the coefficients.

In this case, the common denominator is 8, so multiplying both sides of the equation by 8 gives us 8y = 3x - 32. Moving all the terms to one side, we have 8y - 3x = -32, which is the standard form of the equation.

To transform the equation y = 3/8x - 4 into standard form, subtract 3/8x from both sides and then multiply through by 8 to eliminate the fraction, resulting in -3x + 8y = -32.

The standard form of a linear equation is typically written as Ax + By = C, where A, B, and C are integers and A should not be negative. To convert the equation y = 3/8x - 4 to standard form, you need to manipulate the equation so that it fits the standard form criteria.

Step-by-step, we start by moving the x-term to the left side of the equation:

Therefore, the standard form of the given equation is -3x + 8y = -32.